They're all just valid. You haven't got to sound yet.

'Valid' and 'sound' are predicated of arguments. 'p → p' and the other sentences I listed are sentences, not arguments. Sentences are true or false, not valid or invalid, nor sound or unsound.

Many people have the instict that these are trivial "cambridge" truths and don;t add up to konwing an extra countable infinity of facts every time you learn one empirical fact.

Perhaps, but it will be a pretty huge project to explain 'know' in a way that clearly distinguishes the 'fake' knowledge from the real stuff.